Centers of maximal quotient rings
type: Item
instance of: scholarly article
title: Centers of maximal quotient rings
zbMATH Open document ID: 0661.16001
DOI: 10.1007/BF01190229
author: Pere Ara
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: For a ring R, Z(R) and Q(R) denote the center and the maximal right quotient ring of R, respectively. In the paper the author considers the question: When is Z(Q(R)) the maximal right quotient ring of Z(R)? As the main result it is shown that a von Neumann regular ring R satisfies \(Z(Q(R))=Q(Z(R))\) if and only if R satisfies the following conditions: (1) Any non-zero ideal I of R which has no proper essential extensions in R contains a non-zero central element. (2) \(eZ(R)_{Z(R)}\) is essential in \(Z(eRe)_{Z(R)}\) for each idempotent e of R. Reviewer's comment: The author should make two points clear in stating (1): Do proper essential extensions mean in \(R_ R\), \({}_ RR\) or in both? Does I have to contain an non-zero central element of R or of itself?
reviewed by: Dinh Van Huynh
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16U70
zbMATH DE Number: 4079650
zbMATH Keywords: center
zbMATH Keywords: maximal right quotient ring
zbMATH Keywords: von Neumann regular ring
zbMATH Keywords: essential extensions
zbMATH Keywords: central element
zbMATH Keywords: idempotent
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01190229
OpenAlex ID: W2092507332
description: scientific article; zbMATH DE number 4079650